5.4 Indefinite Integrals and the Net Change Theorem/39

$\int _{1}^{64}{\frac {1+{\sqrt[{3}]{x}}}{\sqrt {x}}}dx$

$\int _{1}^{64}{\frac {1}{x^{1/2}}}$ + $\int _{1}^{64}{\frac {x^{1/3}}{x^{1/2}}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int _{1}^{64}x^{-1/2}+x^{1/3-1/2}} = $\int _{1}^{64}x^{-1/2}+x^{-1/6}$

Add one to the exponents and divide by the new exponent

$\int _{1}^{64}{\frac {x^{1/2}}{\frac {1}{2}}}+{\frac {x^{5/6}}{\frac {5}{6}}}$ = $\int _{1}^{64}2x^{\frac {1}{2}}+{\frac {6}{5}}x^{\frac {5}{6}}$

$2(64)^{\frac {1}{2}}+{\frac {6}{5}}(64)^{\frac {5}{6}}-(2(1)^{\frac {1}{2}}+{\frac {6}{5}}(1)^{\frac {5}{6}})$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 16+38.4 - (2+1.2)}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 54.4 - 3.2}